{"paper":{"title":"Covers of reductive groups and functoriality","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.RT","authors_text":"Tasho Kaletha","submitted_at":"2022-09-28T18:39:42Z","abstract_excerpt":"For a quasi-split connected reductive group $G$ over a local field $F$ we define a compact abelian group $\\tilde\\pi_1(G)$ and an extension $1 \\to \\tilde\\pi_1(G) \\to G(F)_\\infty \\to G(F) \\to 1$ of topological groups equipped with a splitting over $G_\\textrm{sc}(F)$. Any character $x : \\tilde\\pi_1(G) \\to \\mu_n(\\mathbb{C})$ leads to an $n$-fold cover $G(F)_x$ of $G(F)$ via pushout. We define an $L$-group $^LG_x$ for this cover that is generally a non-split extension of $\\textrm{Gal}(F^s/F)$ by $\\hat G$. We prove a refined local Langlands correspondence for $G(F)_x$, assuming it is known for conne"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2209.14357","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2209.14357/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}